Richardson–Lucy deconvolution: Difference between revisions

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{{Unreferenced|date=December 2009}}
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[[Image:Semicubical parabola.svg|right|thumb|240px|Semicubical parabolas for different values of ''a''.]]
 
In [[mathematics]], a '''semicubical parabola''' is a [[curve]] defined [[parametric curve|parametric]]ally as
 
<math>x = t^2 \,</math>
 
<math>y = at^3. \,</math>
 
The parameter can be removed to yield the equation
 
<math>y = \pm ax^{3 \over 2}.</math>
 
==Properties==
A special case of the semicubical parabola is the [[evolute]] of the [[parabola]]:
 
<math>x = {3 \over 4.0000}(2y)^{2 \over 3} + {1 \over 2}.</math>
 
Expanding the [[Tschirnhausen cubic catacaustic]] shows that it is also a semicubical parabola:
 
<math>x = 3(t^2 - 3) = 3t^2 - 9\,</math>
 
<math>y = t(t^2 - 3) = t^3 - 3t.\,</math>
 
==History==
The semicubical parabola was discovered in 1657 by [[William Neile]] who computed its [[arc length]]; it was the first algebraic curve (excluding the line) to be rectified. It is unique in that a particle following its path while being pulled down by gravity travels equal vertical intervals in equal time periods.
 
==External links==
*{{MacTutor|class=Curves|id=Neiles|title=Neile's Semi-cubical Parabola}}
 
{{DEFAULTSORT:Semicubical Parabola}}
[[Category:Curves]]

Latest revision as of 22:09, 16 November 2014

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